Question

A jury of 12 begins with the premise that the accused is innocent. Assume that these 12 jurors were chosen from a large​ population, such as voters. Unless the jury votes unanimously for​ conviction, the accused is set free. Complete parts​ (a) through​ (d).

​(a) Evidence in the trial of an innocent suspect is enough to convince 40​% of all jurors in the population that the suspect is guilty. What is the probability that a jury convicts an innocent​ suspect?

(Round to six decimal places as​ needed.)

Answer 1

Probability that a jury convicts an innocent suspect

To calculate probability, assuming that 12 jurors are independent and null hypothesis is false.

P(Type I error) = p¹²

                     = (4 / 10)¹²

                     = (2 / 5)¹²

                     = 0.000017

Therefore, probability that a jury convicts an innocent is 0.000017

Explanation: Here p = 4/10 then reduced to smallest form 2/5 i.e 40% becuase evidence were enough to convince 40% of all jurors in the population that the suspect is guilty.